Abstract
In this paper, we first show how a certein ordering of vertices, called bicompatible elimination ordering (BCO), of a proper interval graph (PIG) can be used to solve optimally the following problems: finding Hamiltonian cycle in a Hamiltonian PIG, the set of articulation points and bridges, and the single source or all pair shortest paths. We then propose an NC parallel algorithm (i.e., polylogarithmic-time employing a polynomial number of processors) to compute a BCO of a proper interval graph.
Part of this work was done while the first author was with the Dept of Computer and Information Sciences, Univ of Hyderabad and was visiting the Dept of Computer Science and Engineering at the Univ of Texas at Arlington. This work was partally supported by NASA Ames Research Center under Cooperative Agreement Number NCC 2-5359.
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References
C. Been, R. Fagin, D. maier, and M. Yannakakis, On the desirability of acyclic database schemes, J. ACM 30 (1983) 479–513.
P. Buneman, A characterization of rigid circuit graphs, Discrete Mathe. 9 (1974) 205–212.
P. Buneman, The recovery of trees from measures of dissimilarity, in: mathematics in the Archaeological and Historical Sciences, Edinburg University Press, Edinburg (1972) 387–395.
R. Chandrasekharan and A. Tamir, Polylomially bounded algorithms for locating p-centers on a tree, Math. Programming 22 (1982) 304–315.
R. Cole, Parallel merge sort, SIAM J. Comput. 17 (1988) 770–785.
D.R. Fulkerson and O. S. Gross, Incidence matrices and interval graphs, Pacific J. Math. 15 (1965) 835–855.
F. Gavril, The intersection graphs of subtrees in trees are exactly the chordal graphs, J. Combin. Theory, ser B 16 (1974) 47–56.
M.R. Garey and D. S. Johnson, Computers and Intractability: A guide to the theory of NP-completeness, W.H. Freeman and Company (1979).
M. C. Golumbic, Algorithmic graph theory and perfect graphs, Academic press, New York. (1980)
Chin-wen Ho and R.C.T. Lee, Counting clique trees and computing perfect elimination schemes in parallel, IPL 31 (1989) 61–68.
R. E. Jamison and R. Laskar, Elimination orderings of chordal graphs, in “Proc. of the seminar on Combinatorics and applications,” ( K. S. Vijain and N. M. Singhi eds. 1982) ISI, Calcutta, pp. 192–200.
P. N. Klein, Efficient parallel algorithms for chordal graphs, SIAM J. Comput. 25 (1996) 797–827.
C. L. Monma and V. K. Wei, Intersection graphs of paths in a tree, J. Combin. Theory, Ser. B 41 (1986) 141–181.
C. Papadimitriou and M. Yannakakis, Scheduling interval ordered tasks, SIAM J. Comput. 8 (1979) 405–409.
F. S. Roberts, Indifferences graphs, in:“Proof Techniques in Graph Theory”, (F. Harary ed.) 1971, pp.139–146, Academic Press.
D. Rose, A graph theoretic study of the numerical solution of sparse positive definite systems of linear equations: in R. Read ed, Graph Theory and Computing ( Academic Press, New York, 1972) 183–217.
J.R. Walter, representation of chordal graphs as subtrees of a tree, J. Graph Theory 2 (1978) 265–267.
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© 2002 Springer-Verlag Berlin Heidelberg
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Panda, B.S., Das, S.K. (2002). An Efficient Parallel Algorithm for Computing Bicompatible Elimination Ordering (BCO) of Proper Interval Graphs. In: Sahni, S., Prasanna, V.K., Shukla, U. (eds) High Performance Computing — HiPC 2002. HiPC 2002. Lecture Notes in Computer Science, vol 2552. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36265-7_32
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DOI: https://doi.org/10.1007/3-540-36265-7_32
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